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Conformal infinitesimal variations of Euclidean hypersurfaces

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Abstract

In the realm of conformal geometry, we give a parametric classification of the hypersurfaces in Euclidean space that admit nontrivial conformal infinitesimal variations. A parametric classification of the Euclidean hypersurfaces that allow a nontrivial conformal variation was obtained by E. Cartan in 1917. In particular, we show that the class of hypersurfaces studied here is much larger than the one characterized by Cartan.

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Acknowledgements

Miguel I. Jimenez thanks the mathematics department of the Universidad de Murcia for the hospitality during his visit where part of this work was developed. Theodoros Vlachos acknowledges support by the General Secretariat for Research and Technology (GSRT) and the Hellenic Foundation for Research and Innovation (HFRI) Grant No: 133.

Funding

Part of this work is the result of the visit 21171/IV/19 funded by the Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia in connection with the “Jiménez De La Espada” Regional Programme For Mobility, Collaboration And Knowledge Exchange. Marcos Dajczer was partially supported by the Fundación Séneca Grant 21171/IV/19 (Programa Jiménez de la Espada), MICINN/FEDER project PGC2018-097046-B-I00, and Fundación Séneca project 19901/GERM/15, Spain.

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Authors and Affiliations

  1. IMPA—Estrada Dona Castorina, 110, Rio de Janeiro, 22460–320, Brazil

    M. Dajczer

  2. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, SP, 13566-590, Brazil

    M. I. Jimenez

  3. Department of Mathematics, University of Ioannina, Ioannina, Greece

    Th. Vlachos

Authors
  1. M. Dajczer
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  2. M. I. Jimenez
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  3. Th. Vlachos
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Correspondence to Th. Vlachos.

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Dajczer, M., Jimenez, M.I. & Vlachos, T. Conformal infinitesimal variations of Euclidean hypersurfaces. Annali di Matematica 201, 743–768 (2022). https://doi.org/10.1007/s10231-021-01136-z

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  • DOI: https://doi.org/10.1007/s10231-021-01136-z

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